A375798 Expansion of e.g.f. 1/(1 + (log(1 - x^2))/x).

1, 1, 2, 9, 48, 340, 2820, 27720, 309120, 3897936, 54472320, 838918080, 14080651200, 256214724480, 5018771197440, 105361754097600, 2358985057228800, 56124276848640000, 1413738138502609920, 37591686093776855040, 1052149579611011481600

Offset: 0

Author

Seiichi Manyama, Aug 29 2024

Keywords

• nonn

Crossrefs

Cf. A007840, A375799.

Cf. A121452.

Programs

PARI

my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1+log(1-x^2)/x)))

PARI

a(n) = n!*sum(k=0, n\2, (n-2*k)!*abs(stirling(n-k, n-2*k, 1))/(n-k)!);

Formula

a(n) = n! * Sum_{k=0..floor(n/2)} (n-2*k)! * |Stirling1(n-k,n-2*k)|/(n-k)!.